Abstract

We argue that the classic Church’s synthesis problem and the subsequent research that is has spurred is really targeted towards synthesizing transition systems and not programs. We believe that the objective of synthesis must be programs; programs are compact and are the true aim in many synthesis problems, while the transition systems that correspond to them are often large and useless as synthesized artefacts. We reformulate the synthesis of reactive systems in terms of program synthesis, and develop a theory to show that the problem of synthesizing programs over a fixed set of Boolean variables in a simple imperative programming language is decidable for regular ω-specifications. We also present results for synthesizing programs with recursion against both regular specifications as well as visiblypushdown language specifications. Finally, we show applications to program repair, and conclude with open problems in synthesizing distributed programs. 1

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